Sequential effects in magnitude scaling: Models and theory.

Abstract

Research on sequential effects in magnitude scaling is reviewed, and its implications about the adequacy of current time series regression models is discussed. A regression model that unifies what at first appear to be contradictory results is proposed. Theoretical models of judgment and perception are introduced, and their relation to alternative regression models is clarified. A theoretical model of relative judgment that clarifies the role of judgmental error and frames of reference in magnitude scaling is examined in detail. Four experiments that test the model are presented. The results, along with recent results presented by Ward (1987), provide support for the model. The importance of being explicit about the relation of theoretical models to regression models and about the role of error in these models is discussed. In the 1950s, Stevens (e.g., 1956, 1957) popularized a new class of procedures where subjects directly indicated sensation magnitude by responding to presented magnitudes of physical stimuli with numbers (or stimuli). Stevens observed that, when plotted on log-log coordinates, the (geometric) means of responses given to each stimulus intensity showed a linear increase. This led him to conclude that response magnitude, R, is a power function of stimulus magnitude, S: R = o~S ~ (1) where a and 3 are parameters. Stevens also assumed that subjects' responses in magnitude scaling experiments are proportional to sensation magnitude, xI,: R = aT (2)